a nonreceptive prehydrolysis state to a KaiB-receptive posthydrolysis state, which is captured
and stabilized by the CII ring tightened from
S431 autophosphorylation (29). Therefore, the
slow rate of ATP hydrolysis by the CI domain
creates a time delay between CII ring tightening
and CII-CI ring stacking, as well as encoding a
conformational switch needed to bind KaiB. Indeed, mutations that decrease CI ATPase activity
extend clock period to over 40 hours (22). However, because CI ATPase activity does not affect
CII autophosphorylation and autodephosphorylation rates (44), increasing the hypothetical
rate of ATP hydrolysis at the CI domain does
not further shorten the period below ~22 hours
(fig. S4). Hydrolyzing one ATP every ~2 hours,
the CI ATPase tunes the period of the oscillator
from a lower limit of ~22 hours to ~24 hours
(~22 + ~2 hours). Therefore, ATP hydrolysis by
the KaiC CI domain works in concert with the
phosphorylation cycle at the KaiC CII domain to
control KaiB binding and assembly of nighttime
signaling complexes.

KaiB forms a hexameric ring on the CI
domains of KaiC

The KaiBfs-cryst*-KaiCS431E CI interface observed
in the full-length hexamer structure agrees well
with that of the isolated KaiBfs-cryst-CIcryst
heter-odimer (fig. S3B). The hexameric complex is also
consistent with a three-tiered envelope derived
from a 16-Å-resolution cryogenic electron microscopy study (51) (fig. S3C). Monomers of KaiBfs-cryst*
assemble in a ringlike structure on the bottom
face of the KaiCS431E CI domain (Fig. 3), forming
KaiB-KaiB interactions that are likely to promote
the cooperative assembly observed in vitro (50).

The fold-switched C-terminal a3 helix of one
KaiBfs-cryst* protomer interacts with the N-terminal
a1 helix of its clockwise neighbor, increasing
the interfacial area by 206 Å2 over the average
KaiBfs-cryst*-KaiCS431E CI interface area of 983
Å2, adding ~20% more binding surface (Fig. 3C).
Our structure of the hexameric assembly shows
that residue R23 is at the center of the interface
between two adjacent KaiBfs-cryst* subunits, contributing to the electrostatic complementarity
of the KaiB-KaiB interface (Fig. 3, C and D). Consistent with a role in cooperative assembly of
the KaiB-KaiC hexamer (50, 53), an R23A mutation in KaiBAs (superscript “As” denotes proteins
from Anabaena sp.) reduced its binding affinity
for KaiCAs (54). Cooperative assembly of the KaiB-KaiC hexamer may facilitate a robust transition from subjective day to night in the clock by
helping to efficiently capture the rare fold-switched form of KaiB.

Structural basis of cooperative
assembly of the KaiA-KaiB-KaiC
CI complex

The CII domain of KaiC autophosphorylates under stimulation by KaiA during the day (35, 36),
whereas it autodephosphorylates at night when
KaiA is inhibited by KaiB (41), presumably sequestered in a KaiA-KaiB-KaiC complex (39, 55)
(Fig. 1). Both full-length KaiA or KaiADN (fig. S1),
a construct missing the N-terminal domain yet
retaining the ability to stimulate KaiC autophosphorylation and be inhibited by KaiB (28), are
capable of cooperatively forming a KaiA-KaiB-KaiC ternary complex (28) (fig. S5, A to C) and
promoting disassembly of the SasA-KaiC output
signaling complex (28).

To begin to examine molecular determinants
of the KaiADN-KaiBfs-KaiC CI ternary complex in
solution, we collected the methyl-TROSY (
transverse relaxation-optimized spectroscopy) nuclear
magnetic resonance (NMR) spectrum of U-[15N,
2H]-Ile-d-[13C, 1H]–labeled KaiADN in complex with
KaiBfs-cryst and CImono. We found that it was
virtually identical to the spectrum bound to wild-type KaiB and CImono (fig. S5B), demonstrating
that the conformationally locked KaiB variant
and natively captured KaiB both interact with
KaiADN in a similar manner. We also used one
additional mutation (C272S) in KaiADN, hereafter
referred to as KaiAcryst (fig. S1), to prevent intramolecular disulfide formation within the KaiA
dimer during the crystallization process (56). We
then solved a 2.6-Å resolution crystal structure of
the ternary complex KaiAcryst-KaiBfs-cryst-CIcryst
(Fig. 4A), consistent with the stoichiometry of
2 KaiA:1 KaiB:1 CI that we previously observed
in solution (28).

The structure of this isolated ternary complex
demonstrates the molecular basis for cooperative
assembly of KaiA-KaiBfs-KaiC complexes. First,
conserved residue K137 of CIcryst forms a hydrogen bond with Q52 of KaiBfs-cryst and a salt bridge
to E161 of KaiAcryst (Fig. 4B). Second, a triple
junction of interactions was also observed between K137 and Y133 of CIcryst; E161, R162, and
N212 of KaiAcryst; and Q52 and E56 of KaiBfs-cryst.
Finally, the presence of KaiAcryst increased the
number of KaiBfs-cryst-CIcryst hydrogen bonds from
13 to 19 (Figs. 2 and 4), and the KaiBfs-cryst-CIcryst
interfacial surface area from 1000 to 1075 Å2 (Figs.
2 and 4), supporting previous observations that
KaiA induces an increase in apparent affinity of
KaiB for the CI domain (28). This cooperative